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Impossible Cube

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Description

The creation of Impossible Cube is often attributed to the Dutch artist M.C. Escher. The illusion is based on the Necker Cube, which was first described in 1832 by the Swiss crystallographer Louis Albert Necker. Necker noticed that cubes as well as other rhomboids when drawn as wireframes with no cues to depth or orientation could appear to be in two possible orientations. The impossible cube makes use of this effect, often called metastable perception, by including parts of both possible orientations to create a contradictory cube.

Above is one possible way of making an impossible cube, where the edges of the cube that would be closest to the viewer are cut from the viewer’s perspective to reveal the back edges, giving the illusion that they are in front of the closer edges. Even though they are cut, the closer edges still appear to be continuous as they are aligned. Earlier in the 1920’s a group of German psychologists, most notably Max Wertheimer and Wolfgang Köhler, proposed a set of principles that tried to explain related perceptual phenomena. These principles, known as the Gestalt Principles, are commonly known as similarity, continuation, closure, proximity, figure/ground, and symmetry/order (also known as prägnanz). The perceived continuity in the above impossible cube follows the Continuity principle, where objects that seemingly follow the same line are more likely to appear connected to one another.

Necker cube
A Necker Cube

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M.C. Escher's Belvedere

This version of the impossible cube is seen in M.C. Escher’s Belvedere. The main difference between the previous impossible cube is the bottom face of the cube, which appears to be pointing towards the viewer similarly to the top face. The tilt of the camera makes it harder to create the illusion, as the vertical bars of the cube no longer end in the same shape. Both ends are parallelograms that mirror each other horizontally, so the inner line of each bar must be tilted slightly (in this case counter-clockwise from the viewers perspective) for each bar to connect the top of the cube to the bottom. This issue can create inconsistent shading as in the above example, but can be mitigated by smoothing the edges of the impossible cube. The next model is a smoothed version of the Escher-style impossible cube.

Necker cube
The Impossible Cube and Necker Cube Depicted in M. C. Escher's Belvedere

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Isometric Impossible Cubes

The following are two examples of impossible cubes made for an isometric perspective. They both use the edge cutting method like the first impossible cube model, however the second includes an extra piece on the cut vertical bar similar to the Penrose Triangle model.


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References

https://www.newworldencyclopedia.org/entry/Impossible_cube

https://www.newworldencyclopedia.org/entry/Necker_cube

https://www.toptal.com/designers/ui/gestalt-principles-of-design

https://en.wikipedia.org/wiki/Impossible_cube